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Friday, February 10, 2012

This is a difficult exercise, and not only for students. Tom Nudds and I just covered in community ecology the rationale for protected areas planning based not only on representativeness (making sure that all species are protected), but more importantly also on persistence (see his article in Biodiversity and Conservation for a summary of their ideas). If the target areas have all the species you want to conserve, but lack essential components that would ensure their actual persistence through time, representativeness means nothing. Wiersma and Nudds addressed this in their article by focussing on one important component of target areas, minimum reserve area:

"We use candidate protected areas that meet an empirically-derived estimate for a minimum reserve area (MRA) above which no mammal extinctions have been detected from existing protected areas since widespread European settlement, even in parks that have become insularized from the surrounding habitat matrix (Gurd et al. 2001)."

Conservation targets covering (A) 10%, (B) 15%, (C) 20%, and (D) 25% of the marine mammal distributions using the Marxan optimization algorithm to optimize the number of grid cells and its geographic location.

"Our argument previously (3) has been that percentage targets do not allow for any assessment of whether species will persist in areas set aside for conservation, and this critique continues to hold for the analysis by Pompa et al. (1) Their study assessed global representation by using 1° × 1° grid cells, but does not address whether this resolution meets criteria for species persistence."

And this is where it gets ... messy, weird, strange? Pompa and co-authors wrote a reply to this criticism, but actually did not address the lack of including persistence at all. The somehow summarize the single point of the criticism into four separate points:

"Wiersma and Nudds (1) make four main points: (i) the area to be covered by the key conservation sites proposed is a negligible percentage of the ocean; (ii) they doubt the representativeness of our biodiversity patterns; (iii) they question the persistence of the species; and (iv) they claim we do not acknowledge the dynamic nature of ecological systems."

Of the 4 main points identified by Pompa et al. in their reply, (i) and (ii) were side points on the limitations of only including representativeness, and they implicit agree that they did not address point (iv). And it is not that Wiersma and Nudds questioned the persistence (iii) per se of the species, Wiersma and Nudds pointed out, rightly, that this necessary and important condition was not part of the original Pompa et al. conservation strategy.

Instead of acknowledging this directly, they use the scientist cop out, which is so easy to make, but also so unsatisfactory and weak:

Wednesday, February 8, 2012

"A striking feature that has attracted considerable attention is the apparent ubiquity of power-law relationships in empirical data. However, although power laws have been reported in areas ranging from finance and molecular biology to geophysics and the Internet, the data are typically insufficient and the mechanistic insights are almost always too limited for the identification of power-law behavior to be scientifically useful (see the figure). Indeed, even most statistically “successful” calculations of power laws offer little more than anecdotal value."

One argument that they use is that power laws are a statistical feature (or artifact, depending on your point of view) of probabilistic theory:

"Suppose that one generates a large number of independent random variables xi drawn from heavy-tailed distributions, which need not be power laws. Then, by a version of the central limit theorem (CLT), the sum of these random variables is generically power-law distributed."

So finding statistical evidence for power laws (which is not that straight forward, according to the authors) is not even the main problem, finding "a generative mechanism" should be the main focus of scientific pursuit. This is a roundabout way for these mathematicians to suggest the importance of the scientific method, where the context (question, hypothesized causal mechanism, prediction) drives the statistical test that will be tested with new data.

This is one of the biggest hurdles when teaching the scientific method to undergrad (and sometimes graduate) students (and faculty?). We get so many questions that start out with "Is this a good test?", and we always have to get back to them with our standard reply "Context is everything": this test means nothing to us without knowing the context. And now I can refer them to this article as a nice example of the fallacy of focusing on the stats in isolation of the rest.

In addition, the authors also provide a subtle argument against the seductive power of induction. Their concluding sentence reads:

"The most productive use of power laws in the real world will therefore, we believe, come from recognizing their ubiquity (and perhaps exploiting them to simplify or even motivate subsequent analysis) rather than from imbuing them with a vague and mistakenly mystical sense of universality."

I was a scientist, climber (a long time ago), father, and a teacher. And now suddenly these separate aspects of my life got sucked into a vortex, all thanks to reading some passages of Aldo Leopold's "The Land Ethic" for the First Year Seminar course Ingrid and I have designed. These items literally came across my desk (RSS reader, watching TV with the kids, teaching a course) in a 2 day period. And they point out ethical decisions we/I should be making on a daily basis:

should we/I, scientists, actually sample this unique lake that has been separated from the rest of life on earth for who knows how many years?

should we/I "conquer" (Leopold would love this word) a mountain by drilling and placing bolts every couple of feet?

should we/I study, let alone kill, the last individual of a species that could end a war, especially if society (or in this case Chancellor Palpatine, for all the wrong reasons) made this decision?